SELECTED PUBLICATIONS
L. Birbrair, A. Gabrielov.
Lipschitz geometry of real semialgebraic surfaces. Handbook
of Geometry and Topology of Singularities IV, Springer 2023.
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L. Birbrair, M. Brandenbursky, A. Gabrielov.
Lipschitz geometry of surface germs in R^4: metric knots.
Selecta Mathematica (2023) DOI:10.1007/s00029-023-00847-w.
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A. Gabrielov. Classification of generic spherical quadrilaterals.
Arnold Math. J., v.9 (2023) 151-203, DOI:10.1007/s40598-022-00204-3
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L. Birbrair, A. Gabrielov.
Lipschitz geometry of pairs of normally embedded Holder triangles.
Eur. J. Math., 8 (2022) 766-791 PDF
A. Eremenko, A. Gabrielov, G. Mondello, D. Panov.
Moduli spaces for Lame functions and Abelian integrals of the second kind.
Comm. Contemp. Math., 24 (2022) 1-68 PDF
A. Gabrielov, E. Souza.
Lipschitz geometry and combinatorics of abnormal surface germs.
Selecta Mathematica, New Series, 28:1 (2022). DOI:10.1007/s00029-021-00716-4
A. Eremenko, A. Gabrielov.
The space of Schwarz-Klein spherical triangles.
J. Math. Physics, Analysis and Geometry, v.16 (2020) 263-282. PDF
L. Birbrair, A. Gabrielov.
Surface singularities in R^4: First steps towards Lipschitz knot theory.
In: W. Neumann and A. Pichon (Editors),
Introduction to Lipschitz Geometry of Singularities,
157-166, Springer 2020. PDF
A. Eremenko, A. Gabrielov.
PT-symmetric eigenvalues for homogeneous potentials.
J. Math. Phys., v.59, 2018. https://doi.org/10.1063/1.5016390.
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L. Birbrair, A. Gabrielov.
Ambient Lipschitz equivalence of real surface singularities. IMRN, https://doi.org/10.1093/imrn/rnx328, 2018. PDF
Birbrair, L., Fernandes, A., Gabrielov, A., Grandjean, V.
Lipschitz contact equivalence of function germs in R^2.
Annali SNS Pisa, v.17 (2017) 91-92, DOI 10.2422/2036-2145.201503_014.
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A. Eremenko, A. Gabrielov.
Circular pentagons and real solutions of Painleve VI equations.
Comm. Math. Physics (2017), DOI 10.1007/s00220-017-2921-y. PDF
A. Eremenko, A. Gabrielov, A. Hinkkanen.
Exceptional solutions to the Painleve VI equation. J. Math. Physics, 58, 012701 (2017), doi: 10.1063/1.4973440. PDF
A. Gabrielov, N. Vorobjov
On Topological Lower Bounds for Algebraic Computation Trees.
Foundations of Computational Mathematics, v.17 (2017) 61-72, DOI: 10.1007/s10208-015-9283-7. PDF
A. Gabrielov, N. Vorobjov
Topological lower bounds for arithmetic networks.
Computational complexity. (2016) DOI: 10.1007/s00037-016-0145-8.
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A. Eremenko, A. Gabrielov.
Spherical rectangles. Arnold Mathematical Journal, v.2 (2016)
p.463-486. PDF
A. Eremenko, A. Gabrielov, V. Tarasov.
Metrics with conic singularities and spherical quadrilaterals.
Conformal Geometry and Dynamics, v.20 (2016) 128-175.
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A. Eremenko, A. Gabrielov, V. Tarasov.
Spherical quadrilaterals with three non-integer angles.
Journal of Mathematical Physics, Analysis and Geometry, v.12 (2016) 134-167.
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A. Eremenko, A. Gabrielov.
On metrics of curvature 1 with four conic singularities
on tori and on the sphere. Illinois J. Math, v,59 (2015) 925-947. PDF
S. Basu, A. Gabrielov, N. Vorobjov.
Triangulations of monotone families I: Two-dimensional families.
Proc. LMS v.111 (2015) 1013-1051. PDF
A. Eremenko, A. Gabrielov, V. Tarasov.
Metrics with conic singularities and spherical polygons.
Illinois J. Math., v.58 (2014) 739-755.
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A. Eremenko, A. Gabrielov.
Spectral loci of Sturm-Liouville operators with polynomial potentials. In book: Spectral Theory and Differential Equations. V. A. Marchenko 90th Anniversary Collection (editors: E.Khruslov and L.Pastur, AMS Providence, RI, 2014)
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A. Gabrielov, V. Keilis-Borok, S. Olsen and I. Zaliapin.
Predictability of extreme events in a branching diffusion model.
In book: Extreme natural hazards, disaster risks and societal implications.
Cambridge University Press (2014) p.126-142.
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S. Basu, A. Gabrielov, N. Vorobjov.
A Helly-type theorem for semi-monotone sets and monotone maps.
Discrete and Comput Geometry, DOI 10.1007/s00454-013-9540-y (2013)
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S. Basu, A. Gabrielov, N. Vorobjov.
Monotone functions and maps. Revista Real Acad. Cienc. Exactas, Fisicas y Naturales. Ser. A. Matematicas
(RACSAM) v.107 (2013) 5-33.
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S. Basu, A. Gabrielov, N. Vorobjov.
Semi-monotone sets. J. European Math. Soc., v.15 (2013) 635-657.
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A. Eremenko, A. Gabrielov.
Two-parametric PT-symmetric quartic family.
J. Phys. A: Math. Theor. v.45 (2012) 175206. PDF
A. Eremenko, A. Gabrielov.
Quasi-exactly solvable quartic: real algebraic spectral locus.
J. Phys. A: Math. Theor. v.45 (2012) 175205. PDF
P. Alexandersson, A. Gabrielov.
On eigenvalues of the Schrodinger operator
with a complex-valued polynomial potential.
Comput. Methods and Function Theory v.12 (2012) 119-144.
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A. Eremenko, A. Gabrielov.
Singular perturbations of polynomial potentials
in the complex domain with applications to PT-symmetric families.
Moscow Math. J., 11 (2011) 473-503. PDF
A. Eremenko, A. Gabrielov.
Quasi-exactly solvable quartic: elementary integrals and asymptotics.
J. Phys. A: Math. Theor. v.44 (2011) 312001.
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M. Azar, A. Gabrielov.
Some lower bounds in the B. and M. Shapiro conjecture
for flag varieties.
Discr. Comput. Geom. 46 (2011) 636-659, DOI: 10.1007/s00454-010-9314-8.
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A. Eremenko, A. Gabrielov.
Elementary proof of the B. and M. Shapiro conjecture for rational functions.
In: Notions of positivity and the geometry of polynomials, Springer (2011), p.167-178.
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A. Eremenko, A. Gabrielov
Tangencies between holomorphic maps and holomorphic laminations.
Proc. Amer. Math. Soc. v.138 (2010) 2489-2492.
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V. Keilis-Borok, A. Gabrielov, A. Soloviev
Geo-complexity and earthquake prediction.
In: Encyclopedia of Complexity and Systems Science,
Part 7, p.4178-4194, DOI: 10.1007/978-0-387-30440-3_246,
Springer, 2009.
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A. Gabrielov, N. Vorobjov
Approximation of definable sets by compact families, and upper bounds
on homotopy and homology. J. London Math. Soc. v.80 (2009) 45-54, doi: 10.1112/jlms/jdp006
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A. Eremenko, A. Gabrielov
Analytic continuation of eigenvalues of a quartic oscillator.
Comm. Math. Physics
v.287 (2009) 431-457, DOI 10.1007/s00220-008-0663-6
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A. Gabrielov, V. Keilis-Borok, Ya. Sinai, I. Zaliapin
Statistical Properties of the Cluster Dynamics
of the Systems of Statistical Mechanics.
In: Boltzmann's Legacy, ESI Lectures in Mathematics and Physics,
EMS Publishing House, 2008, p.203-216.
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I. Zaliapin, A. Gabrielov, V. Keilis-Borok, H. Wong
Clustering analysis of seismicity and aftershock identification.
Phys. Rev. Letters, v.101 (2008) 018501
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A. Eremenko, A. Gabrielov, B. Shapiro
Zeros of eigenfunctions of some anharmonic oscillators.
Ann. Inst. Fourier, v.58 (2008) 603-624
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A. Eremenko, A. Gabrielov, B. Shapiro
High energy eigenfunctions of one-dimensional Schrodinger operators
with polynomial potentials.
Comput. Methods and Function Theory, v.8 (2008) p.513-529
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A. Gabrielov.
Counter-examples to quantifier elimination for fewnomial
and exponential expressions. Moscow Math. J., v.7 (2007) p.453-460
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A. Gabrielov, D. Novikov, B. Shapiro
Mystery of point charges. Proc. LMS, v.95 (2007) p.443-472; doi:10.1112/plms/pdm012
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A. Gabrielov, V.I. Keilis-Borok, V. Pinsky, O.M. Podvigina,
A. Shapira, V.A. Zheligovsky
Fluid migration and dynamics of a blocks-and-faults system.
Tectonophysics, v.429, p.229-251, 2007.
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A. Eremenko, A. Gabrielov, M. Shapiro. A. Vainshtein
Rational functions and real Schubert calculus.
Proceedings of the AMS, v.134, p.949-957, 2006.
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P. Shebalin, V. Keilis-Borok, A. Gabrielov, I. Zaliapin and
D. Turcotte
Short-term earthquake prediction by reverse analysis of lithosphere
dynamics, Tectonophysics, v.413, p.63-75, 2006.
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Ilya Zaliapin, Henry Wong and Andrei Gabrielov
Hierarchical aggregation in
percolation model, Tectonophysics, v.413, p.93-107, 2006.
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G. Yakovlev, W.I. Newman, D.L. Turcotte, A. Gabrielov
An inverse cascade model for self-organized complexity and
natural hazards. Geophys. J. Int., v.163, p.433-442, 2005.
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I. Zaliapin, H. Wong, A. Gabrielov
Inverse cascade in percolation model: hierarchical description of
time-dependent scaling. Phys. Rev. E, v.71, 066118, 2005.
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A. Gabrielov, N. Vorobjov
Betti numbers of semialgebraic sets defined by quantifier-free formulae.
Discrete and Computational Geometry, v.33, p.395-401, 2005.
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I. Zaliapin, A. Gabrielov, V. Keilis-Borok
Multiscale trend analysis for time series.
Fractals, v.12, p.275-292, 2004.
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V. Keilis-Borok, P. Shebalin, A. Gabrielov, D. Turcotte
Reverse tracing of short-term earthquake precursors.
Physics of the Earth and Planetary Interiors, v.145, p.75-85, 2004.
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A. Gabrielov, N. Vorobjov
Complexity of computations with Pfaffian and Noetherian functions.
In Normal Forms, Bifurcations and
Finiteness Problems in Differential Equations, Kluwer 2004.
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A. Gabrielov, N. Vorobjov, T. Zell
Betti numbers of semialgebraic and sub-Pfaffian sets.
J. London Math. Soc., v.69, p.27-43, 2003.
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A. Gabrielov, T. Zell
On the number of connected components of the relative closure
of a semi-Pfaffian family.
In Algorithmic and Quantitative Real Algebraic Geometry,
AMS 2003, p.65-75.
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A. Gabrielov
Relative closure and the complexity of Pfaffian elimination.
In Discrete and Computational Geometry:
The Goodman-Pollack Festschrift, Springer, 2003.
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A. Eremenko, A. Gabrielov
Pole placement by static output feedback
for generic linear systems.
SIAM J. on Control and Optimization, v.41 p.303-312, 2002.
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A. Eremenko, A. Gabrielov
Degrees of real Wronski maps.
Discrete and Computational Geometry, v.28, p.331-347, 2002.
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A. Eremenko, A. Gabrielov
Counterexamples to pole placement by static output feedback.
Linear Algebra and its Applications, v.351-352, p.211-218, 2002.
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A. Eremenko, A. Gabrielov
Rational functions with real critical points
and the B. and M. Shapiro conjecture in real enumerative geometry.
Annals of Mathematics, v.155, p.105-129, 2002.
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A. Eremenko, A. Gabrielov
The Wronski map and Grassmannians of real codimension 2 subspaces.
Computational Methods and Function Theory, v.1, p.1-25, 2001.
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A. Gabrielov, N. Vorobjov
Complexity of cylindrical decompositions of
sub-Pfaffian sets.
J. Pure and Applied Algebra, v.164, p.179-197, 2001.
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D.L. Turcotte, W.I. Newman, A. Gabrielov.
A statistical physics approach to earthquakes.
In: Geocomplexity and the Physics of Earthquakes,
AGU, 2000, p.83-96.
A. Gabrielov, I. Zaliapin, W.I. Newman, V.I. Keilis-Borok.
Colliding cascades model for earthquake prediction.
Geophys. J. Int., v.143, p.427-437, 2000.
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A. Gabrielov, V. Keilis-Borok, I. Zaliapin, W.I. Newman.
Critical transitions in colliding cascades.
Phys. Rev. E, v.62, p.237-249, 2000.
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A. Gabrielov.
Coxeter-Dynkin diagrams and singularities.
In: Selected Papers of E.B. Dynkin, AMS, 2000, p.367-369.
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A. Gabrielov, W.I. Newman, D.L. Turcotte.
An exactly soluble hierarchical clustering model:
inverse cascades, self-similarity, and scaling.
Phys. Rev. E, 1999, v.60, p.5293-5300.
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A. Gabrielov.
Multiplicity of an analytic function on a trajectory
of a vector field.
In: The Arnoldfest, Fields Inst. Communications , AMS, 1999,
p.191-200.
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A. Gabrielov and A.G. Khovanskii.
Multiplicity of a Noetherian intersection.
In: Geometry of Differential Equations, AMS,
1998, p.119-131.
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A. Gabrielov, F. Jean, J.-J. Risler.
Multiplicity of polynomials on trajectories of polynomial vector fields in C^3.
In: Banach Center Publications, Inst. Math. Polish Ac. Sci., 1998, v.44, p.109-121.
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A. Gabrielov.
Frontier and closure of a semi-Pfaffian set.
J. Discrete and Computational Geometry, 1998, v.19, p.605-617.
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G. Morein, D.L. Turcotte, A. Gabrielov.
On the statistical mechanics of distributed seismicity
Geophys. J. Int., 1997, v.131, p.552-558.
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W.I. Newman, D.L. Turcotte, A. Gabrielov.
Fractal trees with side branching.
Fractals, 1997, v.5, p.603-614
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A. Gabrielov, V. Keilis-Borok, and D.D. Jackson.
Geometric incompatibility in a fault system.
Proc. Natl. Acad. Sci. USA, 1996, v.93, p.3838-3842.
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A. Gabrielov.
Complements of subanalytic sets and existential formulas
for analytic functions.
Inventiones Mathematicae, 1996, v.125, p.1-12.
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W.I. Newman, D.L. Turcotte, and A. Gabrielov.
Log-periodic behavior of a hierarchical failure
model with applications to precursory seismic activation.
Phys. Rev. E, 1995, v.52, p.4827-4835.
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A. Gabrielov.
Multiplicities of zeroes of polynomials on trajectories of
polynomial vector fields and bounds on degree of nonholonomy.
Math. Research Letters, 1995, v.2, p.437-451.
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A. Gabrielov.
Multiplicities of Pfaffian Intersections
and the Lojasiewicz Inequality.
Selecta Mathematica, New Series, 1995, v.1, p.113-127.
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A. Gabrielov and N. Vorobjov.
Complexity of stratifications of semi-Pfaffian sets.
J. Discrete and Computational Geometry, 1995, v.14, p.71-91.
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A. Gabrielov, W.I. Newman, and L. Knopoff.
Lattice models of failure: sensitivity to the local dynamics.
Phys. Rev. E, 1994, v.50, n.1, p.188-197.
W.I. Newman, A. Gabrielov, and D.L. Turcotte, editors.
Nonlinear Dynamics and Predictability of Geophysical Phenomena,
AGU, 1994.
A. Gabrielov.
Avalanches, Sandpiles and Tutte Decomposition.
In: The Gelfand Mathematical Seminars, 1990-1992,
Birkhauser, 1993, p.19-26.
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A. Gabrielov.
Abelian avalanches and Tutte polynomials.
Physica A, 1993, v.195, p.253-274.
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W.I. Newman and A. Gabrielov.
Failure of hierarchical distributions of fiber bundles. I.
Internat. J. of Fracture, 1991, v.50, p.1-14.
A. Gabrielov, T. Levshina, and I. Rotwain.
Block model of earthquake sequence.
Phys. Earth Planetary Interior, 1990, v.61, n.1-2, p.18-28.
A. Gabrielov and V. Keilis-Borok.
Patterns of stress corrosion: geometry of the principal stresses.
Pure and Applied Geophysics, 1983, v.121, n.3, p.477-494.
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M. Caputo, R. Console, A. Gabrielov, V.I. Keilis-Borok, and T.
Sidorenko.
Long-Term Premonitory Seismicity Patterns in Italy.
Geophys. J. R. astr. Soc., 1983, v.75, p.71-75.
A. Gabrielov.
Polar curves and intersection matrices of singularities.
Inventiones Mathematicae, 1979, v.54, p.15-23.
A. Gabrielov.
Combinatorial formulas for Pontryagin classes and GL-invariant cocycles.
Funct. Anal. Appl., 1978, v.12, n.2, p.1-7, in Russian.
English translation: p.75-80.
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M. Alekseevskaya, A. Gabrielov, A. Gvishiani, I. Gel'fand, and E.
Rantsman.
Formal Morphostructural Zoning of mountain territories.
J. of Geoph., 1977, v.43, n.1/2, p.227-235.
D. Fuchs, A. Gabrielov, and I. Gel'fand.
The Gauss-Bonnet theorem and the Atiyah-Patodi-Singer functionals for the
characteristic classes of foliations.
Topology, 1976, v.15, p.165-188.
A. Gabrielov, I. Gel'fand, and M. Losik.
Combinatorial calculation of characteristic classes.
Funct. Anal. Appl., 1975, v.9, n.1, p.54-55, in Russian.
English translation: p.48-49.
Funct. Anal. Appl., 1975, v.9, n.2, p.12-28, in Russian.
English translation: p.103-115.
Funct. Anal. Appl., 1975, v.9, n.3, p.5-26, in Russian.
English translation: p.186-202.
A. Gabrielov, and A. Kushnirenko.
Description of deformations with constant Milnor number for
homogeneous functions.
Funct. Anal. Appl., 1975, v.9, n.4, p.67-68, in Russian.
English translation: p.329-331.
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A. Gabrielov.
Bifurcations, Dynkin diagrams, and modality of isolated singularities.
Funct. Anal. Appl., 1974, v.8, n.2, p.7-12, in Russian.
English translation: p.94-98.
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A. Gabrielov.
Formal relations between analytic functions.
USSR Izv., Ser. Math., 1973, v.37, n.5, p.1056-1090, in Russian.
English translation: p.1056-1088.
A. Gabrielov.
Formal relations between analytic functions.
Funct. Anal. Appl., 1971, v.5, n.2, p.64-65, in Russian.
English translation: p.318-319.
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A. Gabrielov.
On a theorem of Hormander.
Funkt. Anal. Appl., 1970, v.4, n.2, p.18-22, in Russian.
English translation: p.106-109.
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A. Gabrielov.
Projections of semi-analytic sets.
Funct. Anal. Appl., 1968,
v.2, n.4, p.18-30, in Russian.
English translation: p.282-291.
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